A059305 a(n) = pi(Mersenne(n)): index of n-th Mersenne prime.

2, 4, 11, 31, 1028, 12251, 43390, 105097565, 55890484045084135, 10201730804263125133012340

Offset: 1

Author

Reto Keiser (rkeiser(AT)ee.ethz.ch), Jan 25 2001

Keywords

• nonn
• hard
• more

Comments

Similar to A016027, but gives the number of the n-th Mersenne prime (rather than the number of the prime exponent).

A subsequence of A007053 and A086690.

Examples

			Element 2 = 4 because Mersenne2 = (2^3)-1 = 7; 7 is the 4th prime.
		

Links

• Andrew R. Booker, The Nth Prime Page
• C. K. Caldwell, Mersenne Primes
• M. Deleglise and J. Rivat, Computing pi(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp., 65 (1996), 235-245.
• Xavier Gourdon and Pascal Sebah, Counting primes
• Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Crossrefs

Cf. A000043 Mersenne exponents, A000668 Mersenne primes, A016027 pi(mersenne exponents), A001348 Mersenne numbers.

Programs

Mathematica

Array[PrimePi[2^MersennePrimeExponent[#] - 1] &, 8] (* Michael De Vlieger, Apr 21 2019 *)

PARI

LL(e) = if(e==2, return(1)); my(n, h); n = 2^e-1; h = Mod(2, n); for (k=1, e-2, h=2*h*h-1); return(0==h) \\ after Joerg Arndt in A000043
forprime(p=1, , if(LL(p), print1(primepi(2^p-1), ", "))) \\ Felix Fröhlich, Apr 19 2019

Formula

a(n) = A000720(A000668(n))

a(n) = A007053(A000043(n))

A000668(n) = A000040(a(n)). - Omar E. Pol, Jun 29 2012

Extensions

Revised by Max Alekseyev, Jul 20 2007

a(10) from David Baugh, Oct 08 2020